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Properties

Label 47610.p
Number of curves $2$
Conductor $47610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 47610.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47610.p1 47610g2 \([1, -1, 0, -20730, -1031674]\) \(246491883/26450\) \(105719830129350\) \([2]\) \(202752\) \(1.4252\)  
47610.p2 47610g1 \([1, -1, 0, -4860, 114140]\) \(3176523/460\) \(1838605741380\) \([2]\) \(101376\) \(1.0786\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47610.p have rank \(0\).

Complex multiplication

The elliptic curves in class 47610.p do not have complex multiplication.

Modular form 47610.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 4 q^{7} - q^{8} + q^{10} - 4 q^{14} + q^{16} + 4 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.